Mean and Standard Deviation

Date: 03/01/99 at 19:08:48
From: Maria Alejandra Martino
Subject: Mean and Standard Deviation
I have to prove that the formula for the mean and standard deviation
for a binomial distribution are: u = np and s = the square root of
(npq), where n is the total number of trials, p is the probability of
success, and q is the probability of failure, u is the mean and s is
the standard deviation.
I know that u = summation of x*P(X), where P(x) is the probability of
x. I also have that P(x) = (combination of n and x)*[(p)^(x)]*[(q)^(n-
x)] and that p + q = 1 (or, q = 1 - p) so that u = Summation of
{x*(combination of n and x)*[(p)^(x)]*[(q)^(n-x)]} from this part on I
do not know what to do.
Please help me.